There are a few stitches that are reversible. Ribbing, like you mentioned, is a great choice. It's great for a beginning for practicing alternating between knits and purls, too. A good one to start with would be 2x2 rib, which is knit 2 stitches, purl 2 stitches, and repeat. If you use a multiple of 4 stitches (4, 8, 12, 16, etc.) then every row would be K2P2. This is a good choice for a scarf.
Another reversible stitch pattern would be seed stitch. Seed stitch is K1P1 across. If you start with an odd # of stitches, you will K1, P1, etc. across every row. If you start with an even # of stitches, you will K1, P1, etc. across one row, and P1, K1 across the next row - then repeat these two rows and you will get seed stitch.
I just found this stitch library that actually has quite a few reversible stitch patterns:
Welcome to this site, and also to the world of knitting!